Question: Solve for $x$ and $y$ using elimination. ${6x-5y = 4}$ ${-3x+3y = 3}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${6x-5y = 4}$ $-6x+6y = 6$ Add the top and bottom equations together. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {6x-5y = 4}\thinspace$ to find $x$ ${6x - 5}{(10)}{= 4}$ $6x-50 = 4$ $6x-50{+50} = 4{+50}$ $6x = 54$ $\dfrac{6x}{{6}} = \dfrac{54}{{6}}$ ${x = 9}$ You can also plug ${y = 10}$ into $\thinspace {-3x+3y = 3}\thinspace$ and get the same answer for $x$ : ${-3x + 3}{(10)}{= 3}$ ${x = 9}$